A new generalized Frenkel-Kontorova (discrete sine-Gordon) model is proposed which treats a crystal as a set of one-dimensional atomic chains interacting with each other. Here, unlike earlier works, the model does not include the fixed field generated by an external rigid substrate. The two-dimensional version of the model is considered, but the three-dimensional generalization can be easily developed. On the basis of the present interacting atomic chain model a computer simulation of the crowdion (or the anticrowdion) in an anisotropic crystal is made. The calculated results completely agree with analytical results of the elasticity theory.

The well-known Frenkel-Kontorova theoretical model is generalized by including the elastic properties of the three-dimensional medium surrounding the discrete atomic chain considered. The generalized sinuse-Gordon equation (SGE) and the integro-differential equation describing the crowdion in a highly anisotropic crystal are described. The numerical solution of these equations corroborates all the analytical estimates.

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